> Dear all, > > Consider the LP, > min a'x + b'y > s.t. > Px + Qy + r = 0 > x_lb <= x <= x_ub > y_lb <= y <= y_ub > where x,y,r are vector in R^n, P,Q are n x n matrices. > x_lb, x_ub, y_lb, y_ub are bounds of x, y. > > Q1. > My guess is that the intersection of the feasible region of the problem > and the hyper plane (x_k, y_k) where (x_k,y_k) are member of x and y, > is a convex polygon. Is it always true?
Yes, because any hyperplane is a convex set and the intersection of convex sets results in a convex set. Polyhedrality is also preserved. > > Q2. How can one find such intersection area? > ---- > s.s. > It depends on which description of the resulting set you need. One of such descriptions would be simply the original constraints plus the hyperplane equality constraint. _______________________________________________ Help-glpk mailing list [email protected] https://lists.gnu.org/mailman/listinfo/help-glpk
